The invention is based on a brake system having a brake booster. Known prior art brake systems are suitable for reducing undesirable slip when vehicle wheels are braked. If prior art brake systems have a hydraulic brake booster, they can also be expanded into a brake system that automatically sets a minimum distance between a vehicle having this system and the vehicle ahead, and/or into a brake system that reduces the slip of the driving wheels. The disadvantage in such brake systems is that in the anti-slip mode, a pump supplying the brake system must pump undesirably large quantities of pressure medium at high pressure. Such pumps are correspondingly large and expensive and require a large amount of electrical energy. A pump of this kind is also disturbingly noisy.